Computational Methods for Feature Detection in Optical Images

filling in the outermost areas. The kernel must have a total value of zero to ensure that the areas of constant gray values will return a zero edge value. The edge response of a typical LoG kernel is given in Fig. 2.12.

2.3.1.3. Canny edge detection

As with the LoG method, Canny edge detection begins by smoothing the image with a Gaussian function to reduce false edge detection from noise artifacts. The method then uses edge detection kernels (Prewitt or Sobel) in four-directions (0◦, 45◦, 90◦, and 135◦, for example) and finds a gradient magnitude and direction using the method explained in Sec. 2.3.1.1. A nonmaximal suppression step is then employed to determine whether the gradient magnitude is a local maximum in the gradient direction. A high and low threshold is also used to reduce large gradients due to noise. A high threshold is used to ensure the found edges are real, then using directional information from the gradients, edges are traced throughout the image, applying the lower threshold. This method produces a binary image of edge locations, with typically thin edge width due the non-maximal suppression step (Fig. 2.12).

2.3.2. Edge Linkage Methods for Boundary Detection

The boundary detection methods described in Secs. 2.3.1.1 through 2.3.1.3 provide useful initial edge information, but are not robust enough to segment retinal features successfully. The edge pixels are typically corrupted by image noise, illumination effects, and occlusion discontinuities, requiring additional methods to both disregard false edge data and link true feature edges to improve segmentation results. Edge linking methods can also provide the initial steps for segmentation by labeling autonomously linked edges together, thus separating edges from one another so that their structures can be compared to possible features. We will discuss several methods that use edge detection input data to enhance edge linkages for the increasing accuracy of retinal feature segmentation.

2.3.2.1. Local neighborhood gradient thresholding

A simple method to link similar gradients into a single-edge unit is accomplished by comparing magnitude and orientation values. With the domain

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knowledge that retinal region boundary intensity is locally constant and the shape can be considered piecewise linear, we can use simple thresholding of the magnitude and orientation in a local neighborhood to connect like gradients to one another. We will use a gradient magnitude threshold equation

where (x, y) and (x0, y0) are located within some defined local neighborhood, N, and E is a nonnegative threshold value. The gradient angle, α, is found using the equation presented in Sec. 2.3.1, is also compared to the neighborhood

where A is a nonnegative angle threshold. Before implementing the gradient similarity thresholds above, we assume that an initial edge threshold similar to those used in Secs. 2.3.1.1 through 2.3.1.3 has been used. This procedure is recursively repeated throughout the image at every pixel location, with an indexing step used to keep the track of edge labels. Each new edge linkage can be indexed by an integer, which can then be used to find the overall size of each edge. A final minimum/maximum size threshold can be used to erase smaller edges or extremely large edges.

Figure 2.13 displays the multiple steps in the local neighborhood-edge linkage algorithm.

As seen in Fig. 2.13, some edges remain unlinked and some nonedge artifacts remain linked.Additional linking methods can add additional enhancement for more accurate segmentation.

Fig. 2.13. (a) Original grayscale image, (b) image smoothed by Gaussian kernel, (c) edge response using Sobel edge detector, and (d) linked and labeled edges using local neighborhood gradient thresholding.

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Computational Methods for Feature Detection in Optical Images

2.3.2.2. Morphological operations for edge link enhancement

Morphological steps that can increase edge linkages artificially dilate and erode edges using structuring elements defined by the user are commonly used for retinal image feature segmentation.14 A binary image created from an edge detection method will contain broken edges due to soft edges, noise, illumination, or occlusion. The broken edge location will not have similar gradient values to its edge members, thus, methods such as neighborhood gradient thresholding will fail to link the edge. We can use a dilation operation, followed with an erosion step to first link, then thin edges to refine edge structures.

where A is the set of edge locations and B is a structuring element. The

by at least one element. Although this operation is similar to convolution, dilations are based on set operations, as opposed to the arithmetic operations of a convolution mask. We chose a structuring element intuitively, using domain knowledge of the edge structure we are attempting to link, to close gaps while not adding too many false edges. We show the results of edge dilation in Fig. 2.14 using a simple disk-structuring element.

The counterpart of dilation, erosion, is used to reduce edge elements that are created from noise and illumination effects or from a dilation operation.

which indicates that the erosion of A by B is the set of all points z such that B, translated by z, is contained in A. This method is typically used in tandem with dilation operations to either initially reduce edge artifacts or to thin edges. Performing erosion followed by a dilation is referred to as an opening operation, which tends to smooth contours, break narrow edges, and erase thin artifacts. A closing operation is a dilation followed by erosion, which tends to smooth edge contours and fuse narrow edges together. It is also common to perform several erosion and dilation steps using multiple structuring elements to enhance true edges while reducing

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Fig. 2.14. Top: input binary edge image; left: erosion operation; left-center: dilation operation; right-center: opening operation; and right: closing operation.

false edge artifacts. An example of each step of the operation can be seen in Fig. 2.14.

More complex set-theoretic methods can yield better edge linkage and refinement results.8 Because edges can be described as a group of connected components, morphological operations provide useful enhancements to edge linkage challenges, although the parameter adjustment of structuring elements inhibits these methods from providing robust solutions to retinal image feature segmentation. Opening and closing operations have been used for both vasculature and microaneursym segmentation.15,16

2.3.2.3. Hough transform for edge linking

Unlike previous methods, which use local neighborhoods to increase true edge linkage and reduce false edge artifacts, the Hough transform uses a global processing method to link points. As the name implies, the points are transformed from spatial coordinates into a shape-space. This predetermined shape should resemble a feature boundary, such as a circle or ellipse for the optic disk.17 This method can provide boundaries (as shape in the transform) that are robust to noise and breaks in edges. In the case of the line equation transform, we use the normal representation of the line

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